1
$\begingroup$

I have a long expression that has absolute values in the exponent. Some parts of the expression would clearly simplify if one assumes that the power is an odd or even integer. When I give one of this assumption, Mathematica has a very puzzling behaviour. I will give four examples and I would be grateful if someone could explain

Simplify[1+(-1)^Abs[j],{(j+1)/2 ∈ Integers}]

Simplify[t^Abs[j](t+(-1)^Abs[j]),{(j+1)/2 ∈ Integers}]

Simplify[t^Abs[j](1+(-1)^Abs[j]),{(j+1)/2 ∈ Integers}]

Simplify[t^Abs[j](1+t+(-1)^Abs[j]),{(j+1)/2 ∈ Integers}]

The first expression Mathematica rightly simplifies to 0.

For the second expression Mathematica doesn't simplify what is in the brackets, even though it can - maybe Mathematica thinks that if it cannot simplify one absolute value, then it shouldn't simplify any?

The third expression however simplifies, maybe because it manages to simplify to 0?

The fourth expression is the most puzzling. Here Mathematica refuses to simplify what is in the brackets. Presumably it doesn't see it as a simplification? Why?

$\endgroup$
  • $\begingroup$ Welcome to Mathematica.SE! I suggest that: 1) You take the introductory Tour now! 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! 3) As you receive help, try to give it too, by answering questions in your area of expertise. $\endgroup$ – bbgodfrey May 20 '15 at 17:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.